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1
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Feb
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y
201
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Ma
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n
[1
-
3
]
an
d
Dţ
m
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r
a
[
4
-
6
]
f
o
c
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s
ed
o
n
a
p
ar
ticu
lar
s
h
ap
e,
g
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n
b
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ticle.
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tr
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
201
8
:
4
4
1
–
4
4
9
442
f
ield
cr
ea
ted
b
y
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ig
h
v
o
lta
g
e
.
T
h
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m
o
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co
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p
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m
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n
ts
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a
v
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b
ee
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co
n
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u
cted
b
y
[
7
-
1
4
]
.
T
h
e
r
esear
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m
at
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m
a
tical
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ch
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m
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m
[
1
5
-
18
]
.
I
t
en
ab
les
to
ex
a
m
in
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t
h
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s
y
s
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m
b
ased
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n
v
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tu
a
l p
r
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to
ty
p
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g
.
2.
CO
M
P
UT
E
R
M
O
DE
L
O
F
O
F
E
L
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CT
R
I
C
S
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P
ARA
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O
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CYLI
NDR
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CA
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P
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2
.
1
.
Descript
io
n o
f
t
he
P
hy
s
ica
l M
o
del
T
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e
ch
ar
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ed
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e.
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b
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p
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p
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ticles
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t
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s
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ato
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lo
w
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n
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as i
n
to
th
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s
ep
ar
atio
n
s
p
ac
e
(
Fi
g
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r
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1
)
.
T
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ar
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s
p
ac
e
is
cr
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ted
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y
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s
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ial
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o
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es
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a
th
in
b
ar
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p
iece
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f
w
ir
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m
a
y
s
er
v
e
as
t
h
e
i
n
ter
n
a
l
elec
tr
o
d
e)
am
o
n
g
w
h
ic
h
t
h
e
d
ir
ec
t
(
h
er
ein
a
f
ter
DC
)
o
r
t
h
e
alter
n
ati
n
g
(
h
er
ei
n
af
ter
AC
)
elec
tr
ic
f
ield
is
g
e
n
er
ated
d
ep
en
d
in
g
o
n
t
h
e
t
y
p
e
o
f
elec
tr
o
d
e
ch
ar
g
in
g
.
T
h
e
f
o
r
ce
in
ter
ac
tio
n
o
f
t
h
e
elec
tr
ic
f
ield
an
d
th
e
c
h
ar
g
ed
p
ar
ticles
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u
s
es
t
h
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ep
ar
atio
n
an
d
th
e
s
o
r
ti
n
g
o
f
th
e
s
e
p
ar
ticles
f
r
o
m
th
e
air
m
as
s
to
th
e
ex
ter
n
a
l
elec
tr
o
d
e
w
all.
T
h
e
u
s
e
o
f
in
h
o
m
o
g
e
n
e
o
u
s
elec
tr
ic
f
ield
s
ep
ar
ato
r
s
o
r
s
o
r
ter
s
(
as
it
is
in
th
e
s
tu
d
ied
ca
s
e)
u
n
l
ik
e
th
e
h
o
m
o
g
en
eo
u
s
elec
tr
ic
f
ield
eq
u
ip
m
en
t
r
eq
u
ir
es
to
ta
k
e
ac
co
u
n
t
o
f
g
r
ad
ien
t
f
o
r
ce
an
d
its
co
e
f
f
ec
ts
(
to
g
et
h
er
w
it
h
s
o
m
e
o
th
er
f
ac
to
r
s
)
o
n
t
h
e
d
y
n
a
m
ic
s
o
f
a
m
ac
r
o
s
co
p
ic
p
ar
ticle.
T
h
e
ch
o
ice
o
f
th
e
co
o
r
d
in
ate
s
y
s
te
m
a
n
d
t
h
e
k
i
n
e
m
atic
s
c
h
e
m
e
i
s
s
h
o
w
n
i
n
Fig
u
r
e
1
.
A
cc
o
r
d
in
g
to
Fi
g
u
r
e
1
,
th
e
s
y
s
te
m
o
f
f
o
r
ce
s
af
f
ec
ts
t
h
e
m
o
tio
n
o
f
p
a
r
ticles
as s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
Fig
u
r
e
1
.
Kin
e
m
atic
s
c
h
e
m
e
Fig
u
r
e
2
.
S
y
s
te
m
o
f
f
o
r
ce
s
2
.
2
.
Abs
t
ra
ct
Sy
nthesis
o
f
t
he
M
a
t
he
m
a
t
ica
l
m
o
del
Ne
w
to
n
’
s
k
in
e
m
atic
eq
u
atio
n
(
th
e
m
at
h
e
m
atica
l
m
o
d
el)
f
o
r
th
e
m
o
tio
n
o
f
a
m
ac
r
o
s
co
p
ic
p
ar
ticle
in
th
e
s
ep
ar
ato
r
s
p
ac
e
(
s
h
o
w
n
i
n
Fig
u
r
e
1
)
ch
ar
g
ed
b
y
DC
v
o
lta
g
e
tak
e
s
th
e
f
o
llo
w
i
n
g
f
o
r
m
:
3
r
1
r
2
r
2
ln
2
U
2
r
1
r
3
R
0
4
dt
dr
R
6
r
1
r
2
r
ln
qU
2
dt
r
2
d
m
(
1
)
dt
dy
R
6
mg
dt
y
2
d
m
2
(
2
)
I
f
th
e
s
ep
ar
ato
r
is
ch
ar
g
ed
b
y
AC
v
o
lta
g
e,
t
h
e
eq
u
atio
n
s
tak
e
th
e
f
o
r
m
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
Ma
th
ema
tica
l Mo
d
ellin
g
a
n
d
C
o
mp
u
ter S
imu
la
tio
n
A
s
s
is
t in
Desig
n
in
g
N
o
n
-
tr
a
d
itio
n
a
l …
.
(
Mil
a
n
B
ern
á
t
)
443
3
1
2
2
0
2
2
m
r
r
3
0
1
2
0
m
2
2
r
r
r
ln
t
s
i
n
U
2
1
R
4
dt
dr
R
6
r
r
r
ln
t
s
i
n
qU
dt
r
d
m
(
3
)
dt
dy
R
6
mg
2
dt
y
2
d
m
(
4
)
C
au
c
h
y
i
n
itia
l
co
n
d
itio
n
s
f
o
r
th
e
s
o
lu
tio
n
o
f
th
e
s
y
s
te
m
o
f
d
if
f
er
en
tia
l
eq
u
atio
n
s
(
co
n
s
tr
u
c
ted
b
y
u
s
)
f
o
r
th
e
ch
o
s
e
n
co
o
r
d
in
ate
s
y
s
t
e
m
th
e
f
o
llo
w
i
n
g
f
o
r
m
:
r
(
0
)
=
r
0
; v
r
(
0
)
=
v
r0
; y
(
0
)
=
y
0
; v
y
(
0
)
=
v
y0
(
5
)
T
h
e
f
o
llo
w
i
n
g
r
elat
io
n
(
6
)
w
as
tak
en
f
r
o
m
[
1
9
]
w
h
er
e
it h
ad
t
h
e
f
o
r
m
F
g
radGVr
3
1
2
2
2
r
r
3
0
g
r
a
d
G
V
r
r
)
r
r
(
ln
U
)
2
(
)
1
(
R
4
F
(
6
)
No
te:
T
h
e
d
er
iv
atio
n
o
f
t
h
e
r
elatio
n
r
es
u
lt
s
b
y
t
h
e
f
ac
t
th
a
t
th
e
p
ar
ticle
i
n
t
h
e
elec
tr
ic
f
i
eld
is
al
s
o
ch
ar
g
ed
b
y
q
0
.
T
h
e
p
ar
ticle
i
s
af
f
ec
ted
b
y
t
h
e
v
ec
to
r
s
u
m
o
f
f
o
r
ce
s
,
th
e
g
r
ad
ien
t
f
o
r
ce
af
f
ec
ti
n
g
th
e
d
ip
o
le
m
o
m
e
n
t a
cc
o
r
d
in
g
to
(
7
)
an
d
t
h
e
f
o
r
ce
af
f
ec
ti
n
g
th
e
c
h
ar
g
e
g
en
er
at
ed
in
t
h
e
ch
ar
g
in
g
p
r
o
ce
s
s
(
8
)
.
x
)
x
(
E
)
x
(
E
k
F
(
7
)
E
.
q
F
0
E
(
8
)
T
o
s
i
m
p
lify
it,
it
is
co
n
s
id
er
ed
th
at
th
e
v
ec
to
r
E
h
as
o
n
l
y
t
h
e
d
ir
ec
tio
n
x
.
T
h
en
th
e
r
es
u
lt
in
g
f
o
r
ce
is
as f
o
llo
w
s
:
]
x
)
x
(
E
k
q
)[
x
(
E
)
x
(
E
q
x
)
x
(
E
)
x
(
E
k
F
0
0
(
9
)
T
h
e
r
esear
ch
m
et
h
o
d
o
f
m
at
h
e
m
atica
l
m
o
d
ellin
g
a
n
d
co
m
p
u
ter
s
i
m
u
latio
n
h
as
p
r
o
v
e
n
to
b
ec
o
m
e
a
p
o
w
er
f
u
l
ap
p
r
o
ac
h
f
o
r
u
n
d
er
s
t
an
d
in
g
th
e
co
m
p
le
x
it
y
o
f
a
p
h
y
s
ical,
b
io
lo
g
ical,
ch
e
m
ical
s
y
s
te
m
.
I
t
en
ab
les
to
ex
a
m
in
e
t
h
e
s
y
s
te
m
s
b
ased
o
n
v
ir
t
u
al
p
r
o
to
ty
p
i
n
g
.
An
o
r
ig
in
al
p
h
y
s
ical
s
y
s
te
m
is
r
ep
lace
d
b
y
its
co
m
p
u
ter
-
b
ased
v
ir
t
u
al
p
r
o
to
t
y
p
e
to
b
e
u
s
ed
f
o
r
v
ar
io
u
s
co
m
p
u
ter
ex
p
er
im
e
n
t
s
w
h
o
s
e
r
e
s
u
l
ts
ar
e
t
h
en
ap
p
lied
to
t
h
e
o
r
ig
in
al
p
h
y
s
ical
s
y
s
te
m
.
2
.
3
.
Sy
nthesis
o
f
t
he
Co
m
pu
t
er
M
o
del a
nd
S
i
m
ula
t
io
n
B
ased
o
n
t
h
e
m
o
d
el
o
f
t
h
e
s
ep
ar
ato
r
(
s
y
n
t
h
etize
d
ab
o
v
e)
,
th
i
s
w
o
r
k
s
i
m
u
late
s
t
h
e
s
ep
a
r
atio
n
an
d
s
o
r
tin
g
o
f
th
e
p
ar
ticles
w
it
h
v
ar
y
i
n
g
s
ize
a
n
d
w
ei
g
h
t,
b
u
t
w
it
h
id
en
t
ical
m
ater
ial
p
ar
a
m
eter
s
.
I
n
o
r
d
er
to
r
ef
lect
th
e
r
ea
l
tec
h
n
o
lo
g
ical
co
n
d
itio
n
s
w
e
s
e
lecte
d
th
e
p
ar
a
m
eter
s
o
f
t
h
e
p
ar
ticle
1
an
d
th
e
p
ar
ticle
2
w
er
e
s
elec
ted
in
ac
co
r
d
an
ce
w
it
h
th
e
m
ea
s
u
r
e
m
e
n
t
s
ca
r
r
ied
o
u
t in
[
1
9
]
,
[
2
0
]
.
T
h
e
co
n
s
tr
u
cted
s
y
s
te
m
s
o
f
t
h
e
d
if
f
er
en
tial
eq
u
atio
n
s
ar
e
s
y
s
te
m
s
o
f
n
o
n
-
li
n
ea
r
d
if
f
er
en
t
ial
eq
u
atio
n
s
(
d
u
e
to
th
e
n
o
n
li
n
ea
r
d
if
f
er
e
n
tial
E
q
u
atio
n
s
(
1
)
an
d
(
3
)
)
.
Sin
ce
t
h
e
an
al
y
tica
l
s
o
l
u
tio
n
o
f
s
u
c
h
eq
u
atio
n
s
h
as
n
o
t
b
ee
n
p
o
s
s
ib
le,
th
e
ap
p
r
o
x
i
m
atio
n
o
f
th
e
m
e
th
o
d
s
is
t
h
e
o
n
l
y
w
a
y
o
f
s
o
l
v
in
g
t
h
e
g
i
v
e
n
s
et
o
f
eq
u
atio
n
s
.
T
h
e
R
u
n
g
e
-
Ku
t
ta
3
m
et
h
o
d
in
th
e
Ma
tlab
s
o
f
t
w
ar
e
w
er
e
u
s
ed
to
ca
r
r
y
o
u
t
th
e
e
x
ec
u
t
io
n
o
f
th
e
tas
k
s
.
T
h
e
s
y
s
te
m
o
f
t
h
e
d
i
f
f
er
e
n
tial
eq
u
atio
n
s
o
f
m
o
tio
n
(
th
e
m
at
h
e
m
atica
l
m
o
d
el)
w
a
s
s
o
lv
ed
n
u
m
er
icall
y
in
th
e
Ma
tlab
co
m
p
u
tatio
n
al
en
v
ir
o
n
m
en
t
w
it
h
th
e
f
o
llo
w
i
n
g
v
al
u
e
s
:
a.
p
ar
ticle
1
: q
=
0
,
5
∙
1
0
-
8
C
; m
=
1
∙
1
0
-
3
k
g
;
ε
r
=
3
,
5
;
R
=
2
,
5
∙
1
0
-
3
m
;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
201
8
:
4
4
1
–
4
4
9
444
b.
p
ar
ticle
1
: q
=
0
,
4
2
3
2
∙
1
0
-
8
C
;
m
=
0
,
8
0
7
∙
1
0
-
3
k
g
;
ε
r
=
3
,
5
;
R
=
2
,
3
∙
1
0
-
3
m;
Mo
r
eo
v
er
,
Ma
tlab
o
f
f
er
s
an
o
p
p
o
r
tu
n
it
y
f
o
r
th
e
co
m
p
u
tatio
n
al
m
o
d
elli
n
g
o
f
all
t
h
e
r
elati
o
n
s
a
m
o
n
g
th
e
s
tate
v
al
u
es o
f
t
h
e
m
o
d
elle
d
s
y
s
te
m
.
I
n
t
h
e
p
r
esen
t r
esear
ch
,
it a
s
s
i
s
t
s
to
s
o
lv
e
t
h
e
f
o
llo
w
i
n
g
tas
k
s
:
a.
k
in
e
m
at
ics o
f
t
h
e
p
ar
ticle
m
o
ti
o
n
in
t
h
e
m
o
d
elled
p
h
y
s
ical
s
y
s
te
m
,
b.
d
y
n
a
m
ics o
f
th
e
p
ar
ticle
m
o
t
io
n
in
t
h
e
m
o
d
elled
h
y
s
ical
s
y
s
t
e
m
,
an
d
,
c.
v
alu
e
s
ch
ar
ac
ter
izi
n
g
th
e
elec
t
r
ic
f
ield
.
T
h
ese
v
alu
e
s
ar
e
p
r
esen
ted
in
f
o
llo
w
in
g
g
r
ap
h
s
o
f
Fig
u
r
e
3
to
Fig
u
r
e
10
Fig
u
r
e
3
.
Gr
ap
h
ical
r
ep
r
esen
ta
tio
n
o
f
t
h
e
m
o
tio
n
tr
aj
ec
to
r
y
o
f
p
ar
ticle
1
(
r
ed
)
a
n
d
p
ar
ticle
2
(
b
lu
e)
m
o
v
i
n
g
in
t
h
e
s
p
ac
e
o
f
t
h
e
s
ep
ar
ato
r
ch
ar
g
ed
b
y
D
C
v
o
ltag
e
Fig
u
r
e
4
.
Gr
ap
h
ical
r
ep
r
esen
ta
tio
n
o
f
co
m
p
ar
is
o
n
o
f
f
o
r
ce
s
a
f
f
ec
ti
n
g
p
ar
ticle
1
in
th
e
r
elatio
n
F =
f
(
r
)
,
(
DC
v
o
ltag
e)
,
F
g
rad
-
r
ed
,
F
Sr
–
d
ar
k
b
lu
e,
F
E
-
g
r
ee
n
,
F
G
-
lig
h
t b
lu
e
Fig
u
r
e
5
.
Gr
ap
h
ical
r
ep
r
esen
ta
tio
n
o
f
m
o
t
io
n
tr
aj
ec
to
r
y
o
f
p
ar
ticle
1
(
r
e
d
)
a
n
d
p
ar
ticle
2
(
b
lu
e)
m
o
v
i
n
g
in
t
h
e
s
p
ac
e
o
f
t
h
e
s
ep
ar
ato
r
ch
ar
g
ed
b
y
AC
v
o
ltag
e
Fig
u
r
e
6
.
Gr
ap
h
ical
r
ep
r
esen
ta
tio
n
o
f
co
m
p
ar
is
o
n
o
f
f
o
r
ce
s
af
f
ec
ti
n
g
p
ar
ticle
1
in
th
e
r
elatio
n
F =
f
(
r
)
,
(
AC
v
o
lta
g
e)
,
F
g
rad
-
r
ed
,
F
Sr
-
d
ar
k
b
lu
e,
F
E
-
g
r
ee
n
,
F
G
-
li
g
h
t b
lu
e
2
.
3
.
Ana
ly
s
is
a
nd
D
i
s
cu
s
s
io
n o
n t
he
Si
m
u
la
t
io
n R
esu
lt
s
A
p
r
o
p
er
co
n
tr
o
l
o
v
er
t
h
e
s
ep
ar
atio
n
tech
n
o
lo
g
ica
l
p
r
o
ce
s
s
i
s
g
u
ar
an
teed
b
y
ac
h
ie
v
in
g
a
h
i
g
h
d
eg
r
e
e
o
f
co
n
tr
o
l
o
v
er
th
e
k
i
n
e
m
a
ti
cs
an
d
d
y
n
a
m
ics
o
f
t
h
e
p
ar
ti
cles
m
o
tio
n
in
th
e
s
ep
ar
ato
r
s
p
ac
e.
T
h
is
is
n
o
t
w
o
r
k
ab
le
w
i
th
o
u
t
r
ec
o
g
n
izin
g
an
d
id
en
ti
f
y
in
g
t
h
e
ef
f
ec
t
s
o
f
th
e
i
n
d
iv
id
u
al
q
u
alit
y
a
n
d
q
u
a
n
tit
y
f
ac
to
r
s
o
n
t
h
is
m
o
tio
n
.
T
h
is
is
ex
ac
tl
y
w
h
at
t
h
e
cu
r
r
en
t
r
esear
ch
is
ai
m
ed
at.
T
h
e
k
e
y
f
i
n
d
in
g
th
a
t
r
esu
lte
d
f
r
o
m
t
h
e
p
r
esen
t
co
m
p
u
ter
s
i
m
u
latio
n
m
a
y
b
e
d
r
a
w
n
as
f
o
llo
w
s
:
w
h
en
a
n
al
y
zi
n
g
d
y
n
a
m
ic
s
o
f
t
h
e
ch
ar
g
ed
m
ac
r
o
s
co
p
ic
p
ar
ticle
m
o
tio
n
i
n
th
e
s
ep
ar
ato
r
,
it
is
n
ec
es
s
ar
y
t
h
at
also
g
r
ad
ien
t
f
o
r
ce
w
ill
b
e
tak
e
n
in
to
ac
co
u
n
t
b
ec
au
s
e
g
r
ad
ien
t
f
o
r
ce
is
co
m
p
ar
ab
le
w
it
h
t
h
e
o
th
er
f
o
r
ce
in
ter
ac
tio
n
s
(
s
ee
F
ig
u
r
e
4
an
d
Fig
u
r
e
6
)
.
An
o
th
er
i
m
p
o
r
ta
n
t
ac
co
m
p
l
is
h
m
e
n
t
is
t
h
e
r
ev
ea
li
n
g
o
f
t
h
e
p
o
s
s
ib
le
o
cc
u
r
r
en
ce
o
f
cr
itical
o
p
er
atin
g
s
tates
o
f
t
h
e
s
ep
ar
ato
r
p
r
o
v
id
ed
th
at
it
is
c
h
ar
g
ed
b
y
AC
v
o
l
tag
e
(
s
ee
Fi
g
u
r
e
8
.
)
.
T
h
e
b
lu
e
cu
r
v
e
in
Fi
g
u
r
e
8
illu
s
tr
ates
th
e
r
elatio
n
v
r
(
t)
f
o
r
t
=
(
0
;0
,
0
1
s
)
p
r
o
v
id
ed
th
at
φ
0
=
0
°.
T
h
e
r
ed
cu
r
v
e
i
n
Fi
g
u
r
e
8
ill
u
s
tr
ates
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
Ma
th
ema
tica
l Mo
d
ellin
g
a
n
d
C
o
mp
u
ter S
imu
la
tio
n
A
s
s
is
t in
Desig
n
in
g
N
o
n
-
tr
a
d
itio
n
a
l …
.
(
Mil
a
n
B
ern
á
t
)
445
s
a
m
e
r
elat
io
n
p
r
o
v
id
ed
th
at
φ
0
=
1
8
0
°.
T
h
e
co
n
d
u
cted
in
v
e
s
tig
a
tio
n
s
h
o
w
ed
t
h
at
u
n
d
er
t
h
e
co
n
d
itio
n
o
f
φ
0
=
1
8
0
°,
th
e
o
p
er
atio
n
o
f
th
e
s
e
p
ar
ato
r
m
a
y
b
ec
o
m
e
cr
itical.
I
f
th
i
s
is
t
h
e
ca
s
e,
th
e
v
elo
cit
y
o
f
th
e
m
o
tio
n
v
r
(
t)
tak
es
t
h
e
o
p
p
o
s
ite
d
ir
ec
tio
n
in
co
m
p
ar
is
o
n
to
th
e
o
n
e
s
tated
as
th
e
p
o
s
itiv
e
o
n
e.
I
f
th
e
v
e
l
o
cit
y
o
f
th
e
m
o
tio
n
r
ea
ch
ed
a
n
eg
ati
v
e
v
al
u
e
d
u
r
in
g
t
h
e
ti
m
e
t
clo
s
e
to
ze
r
o
,
th
e
p
ar
ticles
w
o
u
ld
ad
h
er
e
to
th
e
w
al
l
o
f
th
e
s
ep
ar
ato
r
.
I
t
w
o
u
ld
th
e
n
d
ep
en
d
u
p
o
n
n
o
th
i
n
g
b
u
t
t
h
e
v
alu
e
v
r
(
0
)
an
d
th
e
ad
h
e
s
i
v
e
co
n
d
i
tio
n
s
.
I
t
is
e
s
s
e
n
tia
l
th
at
t
h
is
o
b
s
er
v
atio
n
w
ill
b
e
tak
en
i
n
to
co
n
s
id
er
atio
n
in
t
h
e
p
r
o
ce
s
s
o
f
d
esig
n
i
n
g
an
d
co
n
s
tr
u
ct
in
g
an
AC
v
o
ltag
e
s
ep
ar
ato
r
.
Fig
u
r
e
7
.
Dep
en
d
en
ce
E
r
=
f
(
r
)
o
n
th
e
tr
aj
ec
to
r
y
o
f
t
h
e
p
ar
ticle
m
o
tio
n
i
n
t
h
e
s
p
ac
e
o
f
th
e
s
ep
ar
ato
r
ch
ar
g
ed
b
y
D
C
v
o
lta
g
e
Fig
u
r
e
8
.
Gr
ap
h
ical
r
ep
r
esen
ta
tio
n
o
f
v
e
lo
cit
y
o
f
p
ar
ticle
1
m
o
tio
n
i
n
t
h
e
s
p
ac
e
o
f
th
e
s
ep
ar
ato
r
(
s
h
o
w
n
i
n
Fi
g
u
r
e
1
)
ch
ar
g
ed
b
y
A
C
v
o
ltag
e.
T
h
e
r
elatio
n
v
r
=
f
(
t)
)
in
th
e
ca
s
e
o
f
ϕ
0
=
0
° (
b
lu
e)
,
in
th
e
ca
s
e
o
f
ϕ
0
=
1
8
0
° (
r
ed
)
Fig
u
r
e
9
.
Gr
ap
h
ical
r
ep
r
esen
ta
tio
n
o
f
t
h
e
m
o
tio
n
tr
aj
ec
to
r
y
o
f
a
p
ar
ticle
m
o
v
i
n
g
in
th
e
i
n
ter
-
elec
tr
o
d
e
s
p
ac
e
s
p
ec
if
ied
ac
co
r
d
in
g
to
Fi
g
u
r
e
1
(
d
ep
en
d
en
c
y
y
=
f
(
r
)
)
.
(
R
ed
co
lo
r
r
ep
r
esen
ts
th
e
tr
aj
ec
to
r
y
in
t
h
e
ca
s
e
o
f
m
o
tio
n
in
t
h
e
f
ield
o
f
s
p
ac
e
ch
ar
g
e,
b
lu
e
co
l
o
r
is
u
s
e
d
f
o
r
th
e
n
o
n
-
ex
is
te
n
ce
o
f
s
p
ac
e
ch
ar
g
e)
Fig
u
r
e
1
0
.
Gr
ap
h
ical
r
ep
r
esen
tatio
n
o
f
t
h
e
in
te
n
s
it
y
co
u
r
s
e
o
f
th
e
elec
tr
ic
f
ield
(
d
ep
en
d
en
c
y
E
r
=
f
(
r
)
-
r
ed
)
in
th
e
i
n
ter
elec
tr
o
d
e
s
p
ac
e
ac
co
r
d
in
g
Fi
g
u
r
e
1
.
(
B
lu
e
co
lo
r
s
h
o
w
s
t
h
e
co
u
r
s
e
i
n
t
h
e
ca
s
e
o
f
n
o
n
-
e
x
i
s
ten
ce
o
f
s
p
ac
e
ch
ar
g
e,
g
r
ee
n
is
f
o
r
“
d
ef
o
r
m
at
io
n
co
n
tr
ib
u
tio
n
”)
T
h
e
m
o
s
t i
m
p
o
r
tan
t r
esear
c
h
c
o
n
tr
ib
u
tio
n
s
ar
e:
a.
T
h
e
im
p
r
o
v
e
m
en
t
o
f
th
e
ex
is
tin
g
r
esear
ch
m
et
h
o
d
s
in
t
h
e
tech
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o
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g
y
o
f
s
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n
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d
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o
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tin
g
(
th
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e
m
p
h
a
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is
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a
s
b
ee
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ctio
n
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o
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a
s
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th
e
m
p
ir
ical
k
n
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e
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g
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e
m
a
in
a
n
d
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r
ac
ticall
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t
h
e
s
o
le
s
o
u
r
ce
o
f
in
f
o
r
m
a
tio
n
)
,
b.
T
h
e
p
ar
allel
s
o
lu
tio
n
o
f
th
e
a
s
p
ec
ts
o
f
t
h
e
k
i
n
e
m
atic
s
,
th
e
d
y
n
a
m
ics,
a
n
d
o
f
t
h
e
elec
tr
ic
f
iel
d
o
f
a
m
o
v
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
201
8
:
4
4
1
–
4
4
9
446
m
ac
r
o
s
co
p
ic
p
ar
ticles (
in
th
e
r
ea
l e
n
v
ir
o
n
m
e
n
t o
f
elec
tr
o
s
tati
c
tech
n
o
lo
g
ies).
Un
li
k
e
th
e
p
ast,
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
o
f
f
er
s
a
m
o
r
e
co
m
p
le
x
s
o
lu
t
io
n
to
th
e
is
s
u
e.
I
t
s
o
lv
es
th
e
is
s
u
e
n
o
t
o
n
l
y
f
r
o
m
t
h
e
v
ie
w
p
o
in
t
o
f
k
in
e
m
atic
s
b
u
t
also
f
r
o
m
t
h
e
v
ie
w
p
o
in
t
o
f
d
y
n
a
m
ic
s
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d
o
f
t
h
e
t
h
eo
r
y
o
f
th
e
elec
tr
o
m
ag
n
etic
f
ie
ld
tak
in
g
i
n
to
ac
co
u
n
t
a
ll
t
h
e
m
aj
o
r
f
ac
t
o
r
s
af
f
ec
ti
n
g
t
h
e
b
allis
tics
o
f
a
p
ar
ticle.
A
cc
o
r
d
in
g
to
it,
th
e
th
en
u
s
ed
e
m
p
ir
ical
m
et
h
o
d
s
w
er
e
ca
p
ab
le
o
f
s
o
lv
in
g
o
n
l
y
t
h
e
k
i
n
e
m
atics
o
f
a
p
ar
ticle
b
u
t
n
o
t
its
d
y
n
a
m
ics,
t
h
er
ef
o
r
e
th
e
m
e
th
o
d
p
r
o
p
o
s
ed
s
ee
m
s
to
b
e
at
th
e
m
o
m
e
n
t
th
e
o
n
l
y
co
m
p
le
x
s
o
lu
tio
n
.
T
h
e
o
v
er
all
r
esu
lt
o
f
t
h
e
p
r
esen
t
co
m
p
u
te
r
s
i
m
u
latio
n
is
t
h
e
k
n
o
w
led
g
e
th
at
th
e
o
p
er
atio
n
o
f
th
e
ex
a
m
in
ed
t
y
p
e
o
f
a
s
ep
ar
ato
r
is
also
b
asicall
y
p
o
s
s
ib
le
w
h
e
n
it
i
s
ch
ar
g
ed
b
y
AC
v
o
lta
g
e
(
it
is
n
ec
es
s
ar
y
to
c
o
n
s
id
er
th
e
p
o
s
s
ib
le
o
cc
u
r
r
en
ce
o
f
cr
itical
o
p
er
atin
g
s
tate
s
)
.
An
alo
g
ica
ll
y
,
i
t
is
p
o
s
s
ib
le
to
s
y
n
t
h
etize
a
co
m
p
u
ter
m
o
d
el
o
f
th
e
s
ep
ar
ato
r
w
it
h
t
h
e
elec
t
r
ic
f
ield
o
f
s
p
atial
c
h
ar
g
e
d
is
tr
ib
u
t
io
n
(
t
h
e
m
o
d
el
i
s
e
v
e
n
m
o
r
e
id
en
t
ical
to
th
e
r
e
al
m
o
d
el)
an
d
to
u
s
e
it
f
o
r
t
h
e
s
i
m
u
latio
n
o
f
p
ar
ticle
s
ep
ar
atio
n
an
d
s
o
r
tin
g
(
i
n
cl
u
d
in
g
p
r
o
g
r
a
m
m
i
n
g
eq
u
ip
m
e
n
t
as
w
ell
as
p
r
o
g
r
a
m
m
in
g
tec
h
n
o
lo
g
y
)
.
T
h
is
p
r
o
b
lem
is
d
ea
lt
w
i
th
i
n
d
etails
i
n
[
1
9
]
,
w
h
er
e
t
h
e
f
o
llo
w
i
n
g
i
s
s
u
e
w
as
s
elec
ted
an
d
d
is
cu
s
s
ed
:
T
h
e
m
o
ti
o
n
o
f
a
p
ar
ticle
o
f
m
ac
r
o
s
co
p
ic
s
ize
in
t
h
e
elec
tr
ic
f
ie
ld
o
f
a
s
p
ac
e
c
h
ar
g
e
(
t
h
e
d
en
s
it
y
o
f
th
e
s
p
ac
e
ch
ar
g
e
is
ρ
=
k
/r
)
as sh
o
w
n
in
t
h
e
Fi
g
u
r
e
1.
T
h
e
s
o
lu
tio
n
o
f
t
h
e
elec
tr
ic
f
ie
ld
ar
e:
0
0
k
)
r
(
V
(
1
0
)
r
0
ε
k
0
ε
r
ρ
dr
dV
r
dr
d
.
r
1
(
1
1
)
Fo
r
b
o
u
n
d
ar
y
co
n
d
itio
n
s
:
0
)
r
(
V
,
r
r
;
U
)
r
(
V
;
r
r
2
2
1
1
(
1
2
)
2
1
0
C
r
ln
C
r
k
V
(
1
3
)
r
C
k
x
V
)
r
(
E
1
0
r
(
1
4
)
E
q
u
atio
n
s
o
f
m
o
tio
n
(
m
at
h
e
m
atica
l
m
o
d
el)
ar
e:
dt
dr
R
6
)
r
(
E
.
q
dt
r
d
m
r
2
2
(
1
5
)
dt
dy
R
6
mg
dt
y
d
m
2
2
(
1
6
)
T
h
e
s
o
lu
tio
n
is
f
o
r
th
e
v
alu
e
s
:
p
.
p
:
r
(
0
)
=
0
,
0
0
5
m
;
v
r
(
0
)
=
1
5
m
/s
;
y
(
0
)
=
0
m
;
v
y
(
0
)
p
ar
ticle:
q
=
1
.
1
0
-
8
C
;
m
=
5
,
5
.
1
0
-
8
kg
;
R
=
0
,
5
.
1
0
-
3
m
r
:
U
=
1
5
0
0
0
V;
r
l
=
0
,
0
0
5
m
;
r
2
=
0
,
5
m
,
k
=
6
.
1
0
-
5
;
C
l
=
1
.
1
0
5
;
s
0
=
8
,
8
5
4
.
1
0
-
1
2
F/
m
d
y
n
a
m
ic
v
is
co
s
it
y
o
f
t
h
e
e
n
v
ir
o
n
m
e
n
t: ƞ
=
1
8
,
1
.
1
0
-
6
k
g
/
m
s
.
3.
CO
M
P
UT
E
R
M
O
DE
L
O
F
O
F
E
L
E
CT
R
I
C
S
E
P
ARA
T
O
R
O
F
CYLI
NDR
I
CA
L
Ma
cr
o
s
co
p
ic
p
ar
ticles
d
if
f
u
s
e
d
in
th
e
s
u
r
r
o
u
n
d
i
n
g
s
o
f
co
r
o
n
ar
y
elec
tr
o
d
e,
w
h
ic
h
is
co
n
n
ec
ted
to
alter
n
ati
n
g
h
ig
h
v
o
lta
g
e,
ar
e
n
o
t
c
h
ar
g
ed
b
y
h
y
p
o
th
e
s
is
.
F
o
r
th
is
r
ea
s
o
n
it
i
s
n
ec
es
s
ar
y
to
cr
ea
te
an
e
lectr
o
-
p
h
y
s
ical
co
n
d
itio
n
f
o
r
t
h
e
cr
e
atio
n
o
f
m
o
n
o
p
o
lar
elec
tr
ical
ch
ar
g
es
in
t
h
e
ar
ea
o
f
f
ee
d
er
e
m
b
o
u
c
h
u
r
e.
O
n
e
p
o
s
s
ib
ilit
y
i
s
to
u
t
ilize
t
h
e
p
h
y
s
ical
p
h
e
n
o
m
en
a
i
n
m
etal
-
d
ielec
t
r
ic
-
g
a
s
b
o
u
n
d
ar
y
.
Du
r
i
n
g
t
h
e
co
n
d
u
cted
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
Ma
th
ema
tica
l Mo
d
ellin
g
a
n
d
C
o
mp
u
ter S
imu
la
tio
n
A
s
s
is
t in
Desig
n
in
g
N
o
n
-
tr
a
d
itio
n
a
l …
.
(
Mil
a
n
B
ern
á
t
)
447
ex
p
er
i
m
e
n
ts
a
co
ax
ial
p
r
ec
ip
it
ato
r
w
ith
f
o
u
r
v
ar
io
u
s
co
r
o
n
ar
y
e
lectr
o
d
es
h
as
b
ee
n
co
n
s
tr
u
c
ted
.
T
h
e
P
VC
tu
b
e
s
er
v
i
n
g
a
s
co
llectin
g
elec
tr
o
d
e
is
th
e
b
asic p
ar
t o
f
p
r
ec
ip
itato
r
.
T
h
in
alu
m
in
u
m
elec
tr
o
d
e
is
attac
h
ed
o
n
th
e
o
u
ts
id
e
o
f
t
h
e
tu
b
e
an
d
it
cr
ea
tes
th
e
g
r
o
u
n
d
elec
tr
o
d
e.
W
ith
in
t
h
e
t
u
b
e
t
h
er
e
i
s
f
i
x
ed
a
t
h
in
co
o
p
er
w
ir
e
s
er
v
in
g
a
s
co
r
o
n
ar
y
e
lectr
o
d
e.
T
h
e
ex
p
er
im
e
n
t
u
s
ed
f
o
u
r
t
y
p
es
o
f
co
r
o
n
ar
y
elec
tr
o
d
e.
O
n
e
o
f
th
e
m
i
s
a
lin
ea
r
elec
tr
o
d
e
an
d
th
e
o
th
er
s
ar
e
s
p
ir
al
elec
tr
o
d
es
w
ith
v
ar
io
u
s
r
is
es
(
Fi
g
u
r
e
11)
.
T
h
e
f
u
n
ct
io
n
o
f
co
r
o
n
ar
y
elec
tr
o
d
e
is
t
h
e
cr
ea
tio
n
o
f
s
tr
o
n
g
i
n
h
o
m
o
g
e
n
eo
u
s
elec
tr
ic
f
ield
.
T
h
is
f
ie
ld
ca
n
b
e
cr
ea
ted
by
e
lectr
o
d
es
w
ith
a
s
m
a
ll
r
ad
iu
s
o
f
b
en
d
.
I
f
t
h
e
co
r
o
n
ar
y
elec
tr
o
d
e
i
s
p
o
s
iti
v
e
,
t
h
e
n
e
w
elec
tr
o
n
s
ar
e
cr
ea
ted
as
co
n
s
eq
u
e
n
ce
o
f
b
o
m
b
i
n
g
a
p
o
in
t
b
y
elec
tr
o
n
s
.
I
f
th
e
co
r
o
n
ar
y
elec
tr
o
d
e
is
n
eg
at
iv
e
,
i
t
is
an
alo
g
ical,
b
u
t
t
h
e
d
if
f
er
e
n
ce
is
th
a
t
t
h
e
av
a
la
n
ch
e
s
e
m
itted
b
y
th
e
n
e
g
ati
v
e
p
o
in
t
ar
e
m
o
v
ed
to
m
o
r
e
h
o
m
o
g
en
eo
u
s
f
ield
,
an
d
as a
co
n
s
eq
u
e
n
ce
th
e
m
o
b
ilit
y
an
d
ab
ilit
y
to
io
n
ize
d
ec
r
ea
s
e.
I
n
t
h
e
elec
tr
ical
p
r
ec
ip
itato
r
s
u
p
p
lied
b
y
alter
n
ati
n
g
v
o
lta
g
e
b
y
u
s
i
n
g
t
h
e
m
etal
co
r
o
n
ar
y
elec
tr
o
d
e
th
e
i
n
s
u
lati
n
g
b
ar
r
ier
is
u
s
ed
as
a
co
llecti
n
g
elec
tr
o
d
e.
Fo
r
m
a
x
i
m
al
e
f
f
icie
n
c
y
it
is
n
e
ce
s
s
ar
y
to
c
h
o
o
s
e
in
s
u
lati
n
g
m
ater
ials
w
it
h
g
r
e
at
v
al
u
e
o
f
r
esi
s
tan
ce
an
d
p
er
m
itti
v
it
y
.
T
h
e
ch
o
ice
o
f
m
ater
ials
d
ep
en
d
s
o
n
an
o
th
er
n
o
n
e
lectr
ical
q
u
a
n
ti
t
y
as
f
o
r
e
x
a
m
p
le
t
h
e
te
m
p
er
at
u
r
e
o
f
f
l
y
i
n
g
g
a
s
,
e
n
o
u
g
h
m
ec
h
an
ica
l
s
o
lid
it
y
a
n
d
etc.
I
n
s
u
lati
n
g
b
ar
r
ier
s
m
u
s
t
n
o
t
ch
a
n
g
e
t
h
eir
m
ec
h
an
ical
an
d
d
ielec
tr
ic
attr
ib
u
tes
u
n
d
er
th
e
i
n
f
l
u
en
ce
o
f
te
m
p
er
atu
r
e.
Fo
r
f
in
d
i
n
g
t
h
e
e
f
f
icien
c
y
o
f
p
r
ec
ip
itato
r
m
o
d
el
th
r
ee
t
y
p
e
s
o
f
d
u
s
t
f
r
o
m
t
h
er
m
al
p
o
w
er
p
lan
t
w
it
h
d
if
f
er
e
n
t
v
a
lu
e
s
o
f
r
esi
s
tan
ce
w
er
e
u
s
ed
.
T
h
e
m
o
d
el
o
f
p
r
ec
ip
itato
r
w
it
h
len
g
t
h
3
0
c
m
h
as
an
ef
f
icie
n
c
y
in
t
h
e
r
an
g
e
o
f
6
0
%
to
9
7
%
f
o
r
ea
ch
o
f
t
h
e
d
u
s
t
t
y
p
e.
P
r
o
v
id
e
a
s
tate
m
e
n
t
t
h
at
w
h
a
t
i
s
e
x
p
ec
ted
,
as
s
tated
in
t
h
e
"
I
n
tr
o
d
u
ctio
n
"
ch
ap
ter
ca
n
u
l
t
i
m
atel
y
r
es
u
lt
in
"
R
esu
l
ts
a
n
d
Dis
cu
s
s
io
n
"
ch
ap
ter
,
s
o
th
e
r
e
is
co
m
p
atib
ili
t
y
.
Mo
r
eo
v
er
,
it
ca
n
also
b
e
ad
d
e
d
th
e
p
r
o
s
p
ec
t
o
f
th
e
d
ev
elo
p
m
en
t
o
f
r
esear
ch
r
e
s
u
l
ts
a
n
d
ap
p
licatio
n
p
r
o
s
p
ec
ts
o
f
f
u
r
th
er
s
t
u
d
ies i
n
to
th
e
n
e
x
t
(
b
ased
o
n
r
esu
lt a
n
d
d
is
cu
s
s
io
n
)
.
Fig
u
r
e
11
.
Sectio
n
s
co
n
f
i
g
u
r
at
io
n
o
f
ca
s
ca
d
e
tu
b
u
lar
p
r
ec
ip
itato
r
s
u
p
p
lied
b
y
alter
n
ati
n
g
h
i
g
h
v
o
ltag
e
T
ab
le
I
.
A
v
er
ag
e
v
al
u
es o
f
e
f
f
i
cien
c
y
f
o
r
ea
ch
o
f
s
ec
tio
n
s
o
f
ca
s
ca
d
e
tu
b
e
-
t
y
p
e
p
r
ec
ip
itato
r
s
u
p
p
lied
b
y
alter
n
ati
n
g
v
o
ltag
e
Ef
f
i
c
i
e
n
c
y
[
%
]
D
u
st
w
i
t
h
ρ
e
=
3
Ω∙m
D
u
st
W
i
t
h
ρ
e
=
13
Ω∙m
D
u
st
w
i
t
h
ρ
e
=
800
Ω
∙
m
L
i
n
e
a
r
e
l
e
c
t
r
o
d
e
7
7
.
77
5
8
.
77
9
8
.
51
2
,
5
c
m s
p
i
r
a
l
e
l
e
c
t
r
o
d
e
8
7
.
10
6
5
.
42
9
0
.
99
4
c
m s
p
i
r
a
l
e
l
e
c
t
r
o
d
e
7
5
.
21
6
1
.
06
9
3
.
07
7
c
m s
p
i
r
a
l
e
l
e
c
t
r
o
d
e
7
2
.
20
5
8
.
79
9
4.
32
4.
CO
NCLU
SI
O
N
C
o
m
p
u
ter
s
i
m
u
la
tio
n
i
s
b
ec
o
m
i
n
g
a
u
s
e
f
u
l
to
o
l
in
t
h
e
i
m
p
l
e
m
en
tatio
n
o
f
th
e
r
esear
c
h
f
in
d
in
g
s
in
to
a
m
an
u
f
ac
t
u
r
in
g
p
r
o
ce
s
s
.
I
t
ca
n
as
s
is
t
i
n
t
h
e
p
r
o
ce
s
s
o
f
d
esig
n
i
n
g
an
d
co
n
s
tr
u
ctin
g
a
n
e
w
t
y
p
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I
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Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
201
8
:
4
4
1
–
4
4
9
448
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cr
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s
is
[
1
9
]
,
[
2
0
]
)
.
ACK
NO
WL
E
D
G
E
M
E
NT
S
T
h
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w
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Gr
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Ag
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Slo
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R
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No
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0
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4
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m
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w
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b
o
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k
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o
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tech
n
ical
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ts
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lo
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o
n
d
ar
y
ed
u
ca
tio
n
.
RE
F
E
R
E
NC
E
S
[1
]
P
a
rk
e
r
K.
R.
(1
9
9
7
):
“
A
p
p
li
e
d
El
e
c
tro
sta
ti
c
Rec
ip
it
a
ti
o
n
.
Bl
a
c
k
ie A
c
a
d
e
mic
a
n
d
Pro
fes
sio
n
a
l,
”
L
o
n
d
o
n
1
9
9
7
,
I
S
BN
0
-
7
5
1
4
-
0
2
6
6
-
4
.
[2
]
M
a
rto
n
K.,
Dţ
m
u
ra
J.:
"
M
o
ti
o
n
o
f
ma
c
ro
sc
o
p
ic
p
a
rticle
s
in
d
ire
c
t
a
n
d
a
lt
e
rn
a
ti
n
g
h
i
g
h
v
o
lt
a
g
e
e
lec
tric
fi
e
ld
"
,
In
.
S
y
m
p
o
siu
m
o
n
Hig
h
Vo
lt
a
g
e
En
g
.
,
G
ra
z
,
V
Ol.
8
p
.
8
3
7
7
-
1
-
4
IS
BN
0
-
7
5
1
4
-
0
2
6
6
-
4.
[3
]
T
i
m
k
o
,
M
.
,
M
a
rto
n
,
K.,
T
o
m
č
o
,
L
.
,
Kira
l
y
,
J.,
M
o
lča
n
,
M
.
,
Ra
jň
a
k
,
M
.
,
Ko
p
č
a
n
sk
ý
,
P
.
,
Cim
b
a
la,
R.
,
S
t
o
ian
,
F
.
,
Ho
lo
tes
c
u
,
S
.
,
T
a
c
u
les
c
u
,
A
.
:
“
M
a
g
n
e
to
-
d
iele
c
tri
c
p
r
o
p
e
rti
e
s
o
f
tran
sf
o
rm
e
r
o
il
b
a
se
d
m
a
g
n
e
ti
c
f
lu
id
s
in
t
h
e
f
re
q
u
e
n
c
y
ra
n
g
e
u
p
to
2
M
Hz
/
-
2
0
1
2
”
,
I
n
:
M
a
g
n
e
to
h
y
d
ro
d
y
n
a
mic
s.
V
o
l
.
4
8
,
n
o
.
2
(2
0
1
2
),
p
.
4
2
7
-
4
3
4
.
-
IS
S
N
0
0
2
4
-
9
9
8
X.
[4
]
Dţ
m
u
ra
J.,
P
e
tráš
J.,
Ba
lo
g
h
J.,
Cim
b
a
la
R.
:
"
Un
c
o
n
v
e
n
ti
o
n
a
l
P
r
e
c
ip
it
a
to
r
S
u
p
p
li
e
d
b
y
A
C
"
,
in
El
e
c
tro
tec
h
n
ika
,
El
e
c
tro
n
ika
,
Au
t
o
ma
t
ica
,
v
o
l
.
5
7
(
2
0
0
9
)
(
n
o
.
2
)
p
.
2
1
-
2
4
,
IS
S
N
1
5
8
2
-
5
1
7
5
.
[5
]
Zak
a
ria
A
l
-
O
m
a
ri,
A
.
Ha
m
z
e
h
,
S
a
d
e
q
A
.
Ha
m
e
d
,
A
.
S
a
n
d
o
u
k
,
G
.
A
ld
a
h
i
m
(2
0
1
5
)
:
“
A
M
a
th
e
m
a
ti
c
a
l
M
o
d
e
l
f
o
r
M
in
im
izin
g
A
d
d
-
On
Op
e
ra
ti
o
n
a
l
Co
st
in
El
e
c
tri
c
a
l
P
o
w
e
r
S
y
ste
m
s
Us
in
g
D
e
sig
n
o
f
E
x
p
e
ri
m
e
n
ts
A
p
p
ro
a
c
h
,
”
in
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
Vo
l
5
,
No
5
,
(2
0
1
5
),
IS
S
N:
2
0
8
8
-
8
7
0
8
.
[6
]
Dz
m
u
ra
,
J.:
“
Na
b
íj
a
teľ
n
o
sť
a
tra
n
sp
o
rt
č
a
stíc
m
a
k
ro
sk
o
p
ick
e
j
v
e
ľ
k
o
sti
v
siln
e
n
e
h
o
m
o
g
é
n
n
o
m
e
le
k
tri
c
k
o
m
p
o
li
,
”
D
ize
rtač
n
á
p
rá
c
a
,
Ko
šic
e
2
0
0
3
.
[7
]
L
.
L
iso
ň
,
I.
Ko
lcu
n
o
v
á
,
J.
Zb
o
j
o
v
sk
ý
,
M
.
K
m
e
c
:
“
Res
e
a
rc
h
o
f
e
lec
tro
p
h
y
sic
a
l
p
r
o
p
e
rties
o
f
o
il
-
p
a
p
e
r
in
su
l
a
ti
o
n
,
”
In
:
E
P
E
2
0
1
4
:
p
ro
c
c
e
d
in
g
s
o
f
t
h
e
2
0
1
4
1
5
th
In
tern
a
ti
o
n
a
l
S
c
ien
ti
f
ic
Co
n
f
e
re
n
c
e
o
n
El
e
c
tri
c
P
o
w
e
r
En
g
in
e
e
rin
g
:
Brn
o
,
1
2
.
-
1
4
.
5
.
2
0
1
4
.
-
Brn
o
:
Un
iv
e
rsity
o
f
Tec
h
n
o
lo
g
y
,
2
0
1
4
P
.
4
0
3
-
4
0
6
.
-
IS
BN
9
7
8
-
1
-
4
7
9
9
-
3
8
0
6
-
3.
[8
]
P
o
d
l
iň
sk
i,
J.
,
Nie
w
u
li
s,
A
.
,
S
h
a
p
o
v
a
l,
V
.
,
M
ize
ra
c
z
y
k
,
J.:
"
El
e
c
tro
h
y
d
ro
d
y
n
a
m
i
c
S
e
c
o
n
d
a
ry
F
lo
w
a
n
d
P
e
rti
c
le
Co
ll
e
c
ti
o
n
Ef
f
icie
n
c
y
in
a
On
e
-
sid
e
r
S
p
ik
e
-
p
late
Ty
p
e
El
e
c
tro
sta
ti
c
P
re
c
ip
it
a
t
o
r"
.
in
IE
EE
T
r
a
n
sa
c
ti
o
n
s
o
n
Die
lec
trics
a
n
d
El
e
c
trica
l
I
n
su
l
a
ti
o
n
.
;
v
o
l.
1
8
(n
o
5
o
c
t
o
b
e
r
2
0
1
1
)
:
p
.
1
4
0
1
-
1
4
0
7
,
IS
S
N:
1
0
7
0
-
9
8
7
8
.
[9
]
A
li
M
a
h
d
a
v
i
Ho
rm
a
t,
Ka
ri
m
F
a
e
z
,
Ze
y
n
a
b
S
h
o
k
o
o
h
i,
M
o
h
a
m
m
a
d
Zah
e
r
Ka
rim
i
(2
0
1
2
):
“
T
h
e
n
e
w
m
e
th
o
d
o
f
Ex
trac
ti
o
n
a
n
d
A
n
a
ly
sis
o
f
No
n
-
li
n
e
a
r
F
e
a
tu
re
s
f
o
r
f
a
c
e
re
c
o
g
n
it
io
n
,”
in
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
E
n
g
in
e
e
rin
g
(IJECE)
V
o
l
2
,
No
6
,
(
2
0
1
2
)
,
IS
S
N:
2
0
8
8
-
8
7
0
8
.
[1
0
]
U
ma
D
(2
0
1
7
)
:
“
M
o
d
e
li
n
g
a
n
d
S
im
u
latio
n
o
f
V
S
I
F
e
d
In
d
u
c
ti
o
n
M
o
to
r
Driv
e
In
M
a
tl
a
b
/S
im
u
li
n
k
,
”
in
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
t
e
r E
n
g
i
n
e
e
rin
g
(IJECE)
V
o
l
7
,
N
o
2
,
(2
0
1
7
),
I
S
S
N:
2
0
8
8
-
8
7
0
8
[1
1
]
F
a
rn
o
o
sh
N.,
A
d
a
m
iak
K.,
Ca
st
l
e
P
.
:
"
Nu
m
e
ric
a
l
Ca
lcu
latio
n
s
o
f
S
u
b
m
icro
n
P
a
rti
c
le
Re
m
o
v
a
l
in
a
S
p
ik
e
-
pl
a
te
El
e
c
tro
sta
ti
c
P
re
c
ip
i
tato
r"
,
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Die
lec
trics
a
n
d
El
e
c
trica
l
In
su
l
a
ti
o
n
.
;
v
o
l.
1
8
(n
o
5
)
o
c
t
o
b
e
r
2
0
1
1
:
p
.
1
4
3
9
-
1
4
5
2
,
IS
S
N:
1
0
7
0
-
9
8
7
8
.
[1
2
]
Du
m
it
ra
n
L
.
M
.
,
Bleja
n
0
.
,
No
ti
n
g
h
e
r
P
.
V.
S
a
m
u
il
a
A
.
D
a
sc
a
l
e
s
k
u
L
.
:
"
P
a
rti
c
le
c
h
a
rg
in
g
in
c
o
m
b
in
e
d
Co
ro
n
a
-
e
lec
tro
sta
ti
c
f
ield
s,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stry
Ap
p
li
c
a
ti
o
n
s
,
v
o
l
4
4
,
n
o
5
.
se
p
tem
b
e
r/o
c
to
b
e
r,
2
0
0
8
,
p
p
.
1
3
8
5
-
1
3
9
0
I
S
S
N 0
0
9
3
-
9
9
9
4
.
(1
9
9
7
)
[1
3
]
M
o
k
h
tari,
G
.
,
No
u
rb
a
k
h
sh
,
G
.
,
Je
n
d
r
u
sik
,
M
.
,
G
a
je
ws
k
i,
J.
B.
,
Š
w
i
e
rc
z
o
k
,
A
.
J.:
"
E
ff
e
c
t
o
f
th
e
p
a
rti
c
le d
ia
m
e
ter
a
n
d
c
o
ro
n
a
e
lec
tro
d
e
g
e
o
m
e
tr
y
o
n
th
e
p
a
rti
c
le
m
i
g
ra
ti
o
n
v
e
lo
c
it
y
in
e
lec
tro
sta
ti
c
p
re
c
ip
it
a
to
rs,
”
in
J
o
u
rn
a
l
o
f
e
lec
tro
sta
ti
c
s,
n
o
5
1
-
52
,
2
0
0
1
,
p
p
.
2
4
5
-
2
5
1
.
IS
S
N 0
3
0
4
-
3
8
8
6
.
[1
4
]
G
ra
ss
N.,
Ha
rt
m
a
n
n
W
.
,
Klo
c
k
n
e
r
M
.
:
"
A
p
p
li
c
a
ti
o
n
o
f
d
if
f
e
r
e
n
t
ty
p
e
s
o
f
h
ig
h
-
v
o
lt
a
g
e
su
p
p
li
e
s
o
n
in
d
u
strial
e
lec
tro
sta
ti
c
p
re
c
ip
it
a
to
rs
,”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
In
d
u
stry
A
p
p
li
c
a
ti
o
n
s,
v
o
l
4
0
,
n
o
6
.
n
o
v
e
m
b
e
r/d
e
c
e
m
b
e
r,
2
0
0
4
,
p
p
.
1
5
1
3
-
1
5
2
0
.
IS
S
N:
0
0
9
3
-
9
9
9
4
.
[1
5
]
Ba
g
in
sk
y
,
I,
(2
0
1
3
)
:
“
M
o
d
e
ll
i
n
g
a
n
d
S
im
u
latio
n
o
f
M
EM
S
El
e
c
tret
V
ib
ra
ti
o
n
-
Driv
e
n
En
e
rg
y
Ha
rv
e
st
e
rs,
”
in
In
ter
n
a
t
io
n
a
l
Rev
iew o
n
M
o
d
e
ll
i
n
g
a
n
d
S
imu
la
ti
o
n
s
(I.
RE.
M
O.S
.
),
V
o
l
6
,
No
1
(
2
0
1
3
).
[1
6
]
Cim
b
a
la,
R.
:
"
T
h
e
Co
m
p
u
tatio
n
o
f
Eq
u
iv
a
len
t
m
o
d
e
l
P
a
ra
m
e
ters
fo
r
Die
lec
tri
c
M
a
teria
ls
"
,
in
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
,
V
o
l
u
m
e
4
8
,
Nu
m
b
e
r
3
-
4
,
Bra
ti
sla
v
a
1
9
9
7
,
p
7
5
-
7
8
.
I
S
S
N 1
3
3
5
-
3
6
3
2
.
[1
7
]
M
.
Ko
ste
re
c
,
J.
Ku
rim
s
k
y
,
M
.
F
o
lt
a
,
S
.
Bu
c
k
o
,
a
Z.
Co
n
k
a
,
"
In
v
e
sti
g
a
ti
o
n
o
f
e
ff
e
c
ts
o
f
n
o
n
-
io
n
izin
g
e
lec
tro
ma
g
n
e
ti
c
fi
e
ld
s
in
te
ra
c
ti
n
g
wit
h
b
i
o
lo
g
ica
l
sy
ste
ms
,
”
P
ro
c
e
e
d
in
g
s
o
f
th
e
8
th
In
tern
a
ti
o
n
a
l
S
c
ien
ti
f
ic
S
y
m
p
o
siu
m
o
n
El
e
c
tri
c
a
l
P
o
w
e
r
En
g
in
e
e
rin
g
(El
e
k
tro
e
n
e
rg
e
ti
k
a
2
0
1
5
)
,
s.
5
6
4
-
5
6
7
,
2
0
1
5
.
[1
8
]
Ku
rim
s
k
ý
,
J.:
"
M
o
d
e
l
o
f
th
e
c
a
v
i
ty
in
th
e
so
li
d
in
su
-
l
a
ti
o
n
a
t
d
if
fer
e
n
t
tem
p
e
ra
tu
re
s"
,
I
n
P
r
o
c
e
e
d
in
g
s
o
f
S
c
ien
ti
f
ic
Co
ll
o
q
iu
m
o
n
Hig
h
V
o
lt
a
g
e
En
g
i
n
n
e
rin
g
,
T
e
c
h
n
ica
l
Un
iv
e
rsity
o
f
Ko
šic
e
,
Ju
n
e
1
1
-
1
2
,
2
0
0
2
.
IS
BN
8
0
-
8
9
0
6
1
-
54
-
0
.
[1
9
]
Be
rn
á
t
M
.
:
“
D
y
n
a
m
ics
o
f
sp
a
c
e
c
h
a
rg
e
s
in
h
ig
h
l
y
n
o
n
-
h
o
m
o
g
h
e
n
e
o
u
s
DC
a
n
d
A
C
f
ield
s,
”
P
h
D
th
e
sis,
F
EI
T
U
Ko
šic
e
2
0
0
0
.
[2
0
]
Be
rn
a
t,
M
.
:
“
Dy
n
a
m
ik
a
p
ries
to
ro
v
ý
c
h
n
á
b
o
j
o
v
v
siln
e
n
e
h
o
-
m
o
g
é
n
n
y
c
h
p
o
li
a
c
h
v
y
t
v
o
re
n
ý
c
h
jed
n
o
-
sm
e
rn
ý
m
a
stried
a
v
ý
m
n
a
p
ä
tí
m
,
”
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
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&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
Ma
th
ema
tica
l Mo
d
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d
C
o
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ter S
imu
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A
s
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(
Mil
a
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á
t
)
449
[2
1
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P
íso
m
n
á
p
rá
c
a
k
d
ize
rta
č
n
e
j
s
k
ú
šk
e
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šic
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.
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.
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i
,
e
t
a
l.
,
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A
n
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a
n
d
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i
m
p
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io
n
o
f
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h
re
e
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Dim
e
n
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n
a
l
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p
a
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o
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re
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se
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o
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r
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In
v
e
rters
,
"
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stri
a
l
El
e
c
tro
n
ics
,
v
o
l.
5
8
,
p
p
.
4
5
0
-
4
6
4
,
F
e
b
2
0
1
1
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
Do
c
.
I
n
g
.
M
i
la
n
B
e
r
n
á
t,
Ph
D
.
w
a
s
b
o
rn
in
K
o
šic
e
,
S
lo
v
a
k
ia,
in
1
9
5
9
.
He
w
a
s
a
w
a
rd
e
d
th
e
In
g
(M
S
c
)
d
e
g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
b
y
th
e
F
a
c
u
lt
y
o
f
El
e
c
tri
c
a
l
En
g
in
e
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rin
g
a
n
d
In
f
o
rm
a
ti
c
s,
T
e
c
h
n
ica
l
Un
iv
e
r
sit
y
o
f
Ko
šic
e
,
in
1
9
8
3
.
He
g
a
in
e
d
th
e
P
h
D.
in
th
e
sc
ien
ti
f
ic
b
ra
n
c
h
2
6
-
34
-
9
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
a
n
d
I
n
f
o
rm
a
ti
c
s
a
t
th
e
F
a
c
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lt
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o
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tri
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a
l
En
g
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g
a
n
d
I
n
f
o
rm
a
ti
c
s,
T
e
c
h
n
ica
l
Un
iv
e
r
sit
y
o
f
Ko
šic
e
,
in
2
0
0
1
(th
e
sis
[1
]
)
a
n
d
th
e
P
h
D.
d
e
g
re
e
in
th
e
sc
ien
ti
f
ic
b
ra
n
c
h
75
-
02
-
9
T
h
e
o
ry
o
f
tec
h
n
ica
l
v
o
c
a
ti
o
n
a
l
su
b
jec
ts
tea
c
h
in
g
a
t
th
e
F
a
c
u
lt
y
o
f
Ed
u
c
a
ti
o
n
,
Co
n
sta
n
ti
n
e
th
e
P
h
il
o
s
o
p
h
e
r
Un
iv
e
rsity
in
Nitra,
in
2
0
0
5
(
th
e
sis
[
2
]
)
.
In
g
.
J
a
r
o
sla
v
Dž
m
u
r
a
,
Ph
D
.
wa
s
b
o
rn
i
n
Ba
rd
e
jo
v
(
S
lo
v
a
k
ia),
o
n
A
p
ril
2
8
,
1
9
7
2
.
He
g
ra
d
u
a
ted
th
e
T
e
c
h
n
ica
l
Un
iv
e
rsit
y
o
f
Ko
ši
c
e
,
F
a
c
u
lt
y
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
a
n
d
In
f
o
rm
a
ti
c
s
in
Ko
šic
e
(S
lo
v
a
k
ia),
in
1
9
9
5
.
He
re
c
e
iv
e
d
t
h
e
P
h
D
d
e
g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
f
ro
m
th
e
T
e
c
h
n
ica
l
Un
iv
e
rsit
y
o
f
Ko
šic
e
(S
lo
v
a
k
ia),
in
2
0
0
2
.
He
is
A
ss
istan
t
P
ro
f
e
ss
o
r
a
t
th
e
T
e
c
h
n
ica
l
Un
iv
e
rsity
o
f
Ko
šic
e
,
in
Ko
šic
e
(S
lo
v
a
k
ia).
His
re
se
a
rc
h
in
tere
sts
c
o
n
c
e
rn
:
h
ig
h
v
o
lt
a
g
e
e
n
g
in
e
e
rin
g
,
e
lec
tro
sta
ti
c
s an
d
sm
a
rt
e
lec
tri
c
in
sta
ll
a
ti
o
n
.
P
a
e
d
Dr.
Ľu
b
o
m
ír
Ţáč
o
k
,
P
h
D.
w
a
s
b
o
rn
in
S
tará
Ľu
b
o
v
ň
a
,
S
lo
v
a
k
ia,
in
1
9
7
5
.
He
g
ra
d
u
a
ted
1
9
9
8
,
tea
c
h
in
g
g
e
n
e
ra
l
su
b
jec
ts
a
t
P
re
šo
v
,
Un
iv
e
rsit
y
in
P
re
šo
v
.
In
2
0
0
6
,
h
e
su
c
c
e
ss
f
u
ll
y
a
n
d
w
a
s
a
wa
rd
e
d
P
h
D
d
e
g
re
e
in
a
sc
ien
ti
f
ic
d
isc
ip
li
n
e
th
e
o
ry
o
f
tea
c
h
in
g
tec
h
n
i
c
a
l
v
o
c
a
ti
o
n
a
l
su
b
jec
ts.
Ľu
b
o
m
ír
Ţáč
o
k
w
o
rk
s
a
s
a
n
a
ss
istan
t
p
ro
f
e
ss
o
r
a
t
th
e
De
p
a
rt
m
e
n
t
o
f
Tec
h
n
ics
a
n
d
Tec
h
n
o
lo
g
y
F
P
V
U
M
B
in
Ba
n
sk
á
By
stric
a
.
He
is
f
o
c
u
se
d
to
th
e
f
ield
n
a
m
e
d
a
s
i
m
p
le
m
e
n
tatio
n
o
f
in
f
o
rm
a
ti
o
n
a
l
a
n
d
c
o
m
m
u
n
ica
ti
o
n
a
l
tec
h
n
o
l
o
g
ies
in
to
th
e
p
r
o
c
e
ss
o
f
e
d
u
c
a
ti
o
n
in
th
e
tec
h
n
ica
l
su
b
jec
ts.
He
is
a
n
a
u
th
o
r
o
f
two
sc
ien
ti
f
ic
m
o
n
o
g
ra
p
h
ies
a
n
d
o
n
e
o
f
th
e
m
w
a
s
p
u
b
l
ish
e
d
in
Uk
ra
in
e
,
P
o
lan
d
a
n
d
L
it
h
u
a
n
ia.
P
ro
f
e
ss
io
n
a
l
a
n
d
sc
ien
ti
f
ic
p
u
b
li
c
a
ti
o
n
s
w
e
re
p
u
b
li
sh
e
d
in
th
e
S
lo
v
a
k
,
b
u
t
a
lso
i
n
t
h
e
in
ter
n
a
ti
o
n
a
l
jo
u
r
n
a
ls.
In
g
.
J
a
n
P
a
v
l
o
v
k
i
n
,
Ph
D.
w
a
s
b
o
rn
i
n
Kru
p
in
a
(
S
lo
v
a
k
re
p
u
b
l
ic),
o
n
M
a
y
2
5
,
1
9
5
5
.
He
g
ra
d
u
a
ted
th
e
S
l
o
v
a
k
Tec
h
n
ica
l
Un
iv
e
rsit
y
in
Bra
ti
sla
v
a
,
F
a
c
u
lt
y
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
a
n
d
C
o
m
p
u
ter
S
c
ien
c
e
in
Bra
ti
sla
v
a
(S
lo
v
a
k
Re
p
u
b
li
c
),
i
n
1
9
8
1
–
T
e
c
h
n
i
c
a
l
C
y
b
e
rn
e
ti
c
s
–
A
u
to
m
a
ti
o
n
T
e
c
h
n
o
l
o
g
y
.
He
r
e
c
e
i
v
e
d
th
e
P
h
.
D.
d
e
g
re
e
in
A
u
to
m
a
ti
o
n
a
n
d
Co
n
tro
l
f
ro
m
th
e
S
lo
v
a
k
T
e
c
h
n
ica
l
Un
iv
e
rsit
y
in
Bra
ti
sla
v
a
,
F
a
c
u
lt
y
o
f
El
e
c
tri
c
a
l
En
g
in
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e
rin
g
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n
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Co
m
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ter
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ien
c
e
in
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sla
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(S
lo
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k
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p
u
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li
c
),
i
n
2
0
0
5
.
He
is
As
sista
n
t
P
r
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ss
o
r
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th
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p
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rtme
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t
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ies
a
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th
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F
a
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lt
y
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f
Na
tu
ra
l
S
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s,
M
a
tej
Be
l
U
n
iv
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(S
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k
Re
p
u
b
li
c
).
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re
se
a
rc
h
in
tere
sts
c
o
n
c
e
rn
:
o
f
El
e
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c
a
l
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g
in
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rin
g
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d
it
s
a
p
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ti
o
n
s
t
o
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e
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ry
o
f
Co
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tec
h
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v
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c
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g
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c
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RN
D
r
.
Re
n
á
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e
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n
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to
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s
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p
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li
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a
y
2
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,
1
9
5
5
.
He
g
ra
d
u
a
ted
th
e
S
lo
v
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h
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Un
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in
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ti
sla
v
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a
c
u
l
ty
o
f
El
e
c
tri
c
a
l
En
g
in
e
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rin
g
a
n
d
Co
m
p
u
ter
S
c
ien
c
e
in
Bra
ti
sla
v
a
(
S
lo
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k
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p
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b
li
c
),
in
1
9
8
1
–
T
e
c
h
n
ica
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Cy
b
e
rn
e
ti
c
s
–
A
u
to
m
a
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T
e
c
h
n
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lo
g
y
.
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r
e
c
e
i
v
e
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th
e
P
h
.
D.
d
e
g
re
e
in
A
u
to
m
a
ti
o
n
a
n
d
Co
n
tro
l
f
ro
m
th
e
S
lo
v
a
k
T
e
c
h
n
ica
l
Un
iv
e
rsit
y
in
Bra
ti
sla
v
a
,
F
a
c
u
lt
y
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
a
n
d
Co
m
p
u
ter
S
c
ien
c
e
in
Bra
ti
sla
v
a
(S
lo
v
a
k
Re
p
u
b
li
c
),
i
n
2
0
0
5
.
He
is
As
sista
n
t
P
r
o
f
e
ss
o
r
a
t
th
e
De
p
a
rtme
n
t
o
f
Tec
h
n
o
lo
g
y
a
n
d
tec
h
n
o
l
o
g
ies
a
t
th
e
F
a
c
u
lt
y
o
f
Na
tu
ra
l
S
c
ien
c
e
s,
M
a
tej
Be
l
U
n
iv
e
rsit
y
(S
lo
v
a
k
Re
p
u
b
li
c
).
His
re
se
a
rc
h
in
tere
sts
c
o
n
c
e
rn
:
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
a
n
d
it
s
a
p
p
li
c
a
ti
o
n
s
t
o
t
h
e
T
h
e
o
ry
o
f
Co
n
tro
l
s
y
ste
m
s an
d
tec
h
n
ica
l
v
o
c
a
ti
o
n
a
l
su
b
jec
ts
tea
c
h
in
g
.
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